A368019 a(n) is the permanent of the n-th order Hankel matrix of Catalan numbers M(n) whose generic element is given by M(i,j) = A000108(i+j+1) with i,j = 0, ..., n-1.

1, 1, 9, 979, 1417675, 28665184527, 8325587326635565, 35389363346700690999467, 2230867495754739989535874468003, 2106171270085074740753132799048111935155, 30007898337707083458776293190436074888346472515407, 6491219550166075876771081259839537013093735814742318424677245

Offset: 0

Author

Stefano Spezia, Dec 08 2023

Keywords

• nonn

Examples

			a(4) = 1417675:
   1,  2,   5,  14;
   2,  5,  14,  42;
   5, 14,  42, 132;
  14, 42, 132, 429.
		

Links

• Arthur T. Benjamin, Naiomi T. Cameron, Jennifer J. Quinn, and Carl R. Yerger, Catalan determinants-a combinatorial approach, Congressus Numerantium 200, 27-34 (2010). On ResearchGate.
• M. E. Mays and Jerzy Wojciechowski, A determinant property of Catalan numbers. Discrete Math. 211, No. 1-3, 125-133 (2000).
• Wikipedia, Hankel matrix.

Crossrefs

Cf. A000108.

Cf. A278843, A368012, A368021, A368022, A368023, A368024, A368025.

Column k=1 of A368026.

Programs

Mathematica

Join[{1},Table[Permanent[Table[CatalanNumber[i+j+1],{i,0,n-1},{j,0,n-1}]],{n,11}]]

PARI

C(n) = binomial(2*n,n)/(n+1); \\ A000108
a(n) = matpermanent(matrix(n,n,i,j,C(i+j-1))); \\ Michel Marcus, Dec 09 2023

Formula

Det(M(n)) = 1 (see Mays and Wojciechowski, 2000).